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Minimizing travelling waves for the Gross-Pitaevskii equation on
André de Laire, Philippe Gravejat, Didier Smets
We study the Gross-Pitaevskii equation in dimension two with periodic conditions in one direction, or equivalently on the product space where $L >…
The cubic Schr{ö}dinger regime of the Landau-Lifshitz equation with a strong easy-axis anisotropy
André De Laire, Philippe Gravejat
We pursue our work on the asymptotic regimes of the Landau-Lifshitz equation for bi-axial ferromagnets. We put the focus on the cubic Schr{ö}dinger equation, which is known to desc…
Traveling waves for some nonlocal 1D Gross-Pitaevskii equations with nonzero conditions at infinity
André de Laire, Pierre Mennuni
We consider a nonlocal family of Gross-Pitaevskii equations with nonzero conditions at infinity in dimension one. We provide conditions on the nonlocal interaction such that there…
Nonexistence of traveling waves for a nonlocal Gross-Pitaevskii equation
André de Laire
We consider a Gross-Pitaevskii equation with a nonlocal interaction potential. We provide sufficient conditions on the potential such that there exists a range of speeds in which n…